Interestingly enough, the answer to your question is a secret!

It's based on expertise in a tag and activity on the site, but that's about as far as we know.

David Fullerton posted this on MSE:

The exact criteria probably won't be announced, because we don't want people to game it. It's not a straight "greater than X reputation", but based on expertise in a tag, and your recent activity on the site.

You can also get invited by going to this page and clicking the "Request an Invitation" button.

Interestingly enough, the answer to your question is a secret!

It's based on expertise in a tag and activity on the site, but that's about as far as we know.

David Fullerton posted this on MSE:

The exact criteria probably won't be announced, because we don't want people to game it. It's not a straight "greater than X reputation", but based on expertise in a tag, and your recent activity on the site.

You can also get invited by going to this page and clicking the "Request an Invitation" button.